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Define a family ℋ of hash functions from a finite set U to a finite set B to be ϵ-universal if for all pairs of distinct elements k and l in U Pr{h(k)=h(l)} ≤ϵwhere the probability is taken over the drawing of hash function h at random from the family ℋ. Show that an ϵ-universal family of hash functions must have ϵ≥(1)/(|B|)-(1)/(|U|) | Numerade
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Prove that if S1 is a nonempty subset of the finite set S2, and S1 is linearly dependent, then so is S2.
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Problem 5 (10 pts) An important problem encountered by personnel directors and others faced with the selection ofthe best in a finite set of elements is exemplified by the following scenario. From group of 20 engineers, including 5 Ph.D engineers, 10 are randomly selected for employment: What is the probability that the 10 selected include(a) (5 pts) all the 5 Ph.D. engineers in the group of 202(b) (5 pts) only one Ph.D. engineer in the group of 202Problem 6 (15 pts) An oil drilling compan
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